It is worth noting that if by using Itô's lemma we re-write (REF ) for the stochastic variable \(r_t\) , the resulting dynamics
can be recognized as the stochastic Verhulst or stochastic logistic model, which are well-known in the population dynamics and epidemiology; see, eg., [1]}, [2]}, [3]} and references therein. For more information, see [4]}.
